Sense and Sensitivity - I. Uncertainty analysis of the gas-phase chemistry in AGB outflows

TL;DR

This work presents the first uncertainty analysis of gas-phase chemistry in AGB circumstellar envelopes using the Rate22 network, propagating rate-uncertainties through $N=10{,}000$ Monte Carlo realizations to quantify impacts on fractional abundances and column densities for both C-rich and O-rich outflows across three densities. By treating rate coefficients as lognormal variables with accuracy-based widths, the study isolates how chemistry—not photodissociation rates alone—limits envelope sizes and shapes, particularly for parent species, and how daughter-species predictions exhibit moderate dispersions (averaging around $\sim 10\%$ for peak abundances and a few to tens of percent for column densities). The results show that chemical uncertainty can alter the CO envelope and thus the retrieved mass-loss rates by factors up to about $2$, while most predictions remain well captured by the standard, smooth CSE model; nonetheless, certain observations (e.g., dust-gas interactions, porosity, and companion UV fields) require additional physical or chemical complexity. Overall, the paper provides a framework to gauge when added complexity is needed and highlights the non-propagation of errors across radii due to the changing dominant chemistry in the outflow. This uncertainty-aware perspective informs both interpretation of observations and future model development in CSE astrochemistry.

Abstract

Chemical reaction networks are central to all chemical models. Each rate coefficient has an associated uncertainty, which is generally not taken into account when calculating the chemistry. We performed the first uncertainty analysis of a chemical model of C-rich and O-rich AGB outflows using the Rate22 reaction network. Quantifying the error on the model predictions enables us to determine the need for adding complexity to the model. Using a Monte Carlo sampling method, we quantified the impact of the uncertainties on the chemical kinetic data on the predicted fractional abundances and column densities. The errors are caused by a complex interplay of reactions forming and destroying each species. Parent species show an error on their envelope sizes, which is not caused by the uncertainty on their photodissociation rate, but rather the chemistry reforming the parent after its photodissociation. Using photodissociation models to estimate the envelope size might be an oversimplification. The error on the CO envelope impacts retrieved mass-loss rates by up to a factor of two. For daughter species, the error on the peak fractional abundance ranges from a factor of a few to three orders of magnitude, and is on average about 10\% of its value. This error is positively correlated with the error on the column density. The standard model suffices for many species, e.g., the radial distribution of cyanopolyynes and hydrocarbon radicals around IRC +10216. However, including spherical asymmetries, dust-gas chemistry, and photochemistry induced by a close-by stellar companion are still necessary to explain certain observations.

Figures (17)

• Figure 1: Distribution of the Rate22 reaction rates per associated accuracy and the method by which the rate has been determined. Percentages are indicated in colour and as printed in each category. An accuracy of A represents an error of less than 25%, B less than 50%, C within a factor of 2, D within an order of magnitude, and E a highly uncertain error The percentage of rates for each method and accuracy are indicated at each row and column, respectively.
• Figure 2: Fractional abundance w.r.t. H2 of the C-rich (top) and O-rich (bottom) parent species in an outflow with $\dot{M} = 10^{-6}\ \mathrm{M}_\odot\ \mathrm{yr}^{-1}$. The dashed line shows the fiducial model prediction using Rate22. The solid line shows the mean abundance $\langle \log X(r)\rangle$ of the Monte Carlo sample of reaction networks. The shaded region contains 95.4% of all predicted profiles and corresponds to the error $\Delta \log X(r)$ on the mean abundance.
• Figure 3: Envelope sizes and their radial extents for the parent species in C-rich (left) and O-rich (right) outflows. Different colours indicate different mass-loss rates. Species in common are shown near the top, differing species near the bottom. Square: envelope size as predicted using Rate22. Circle: mean envelope size obtained from the Monte Carlo sample of reaction networks. Envelopes that are not well-constrained are marked by a triangle. These have a range in radial extent (ratio between the largest and smallest radial extent) larger than 3.
• Figure 4: Fractional abundance w.r.t. H2 of a selection of daughter species in a C-rich (top) and O-rich (bottom) outflow with $\dot{M} = 10^{-6}\ \mathrm{M}_\odot\ \mathrm{yr}^{-1}$. The dashed line shows the fiducial model prediction using Rate22. The solid line shows the mean abundance $\langle \log X(r)\rangle$ of the Monte Carlo sample of reaction networks. The shaded region contains 95.4% of all predicted profiles and corresponds to the error $\Delta \log X(r)$ on the mean abundance.
• Figure 5: Scatter plots for all daughter species in a C-rich outflow with $\dot{M} = 10^{-6}\ \mathrm{M}_\odot\ \mathrm{yr}^{-1}$. Left: mean peak fractional abundance versus the error on the peak abundance. Middle: mean column density versus its error. Right: dispersion of the column density versus the dispersion of the peak fractional abundance. The species have a column density of at least $10^{5}$ cm$^{-2}$, removing those that do not contribute to the overall chemistry. The shaded contours show the kernel density estimation of the point distribution, with three intensity levels indicating regions of increasing point concentration.